The specific heat of a substance varies as (3t^(2) + t) xx 10^(-3) "cal"//g- ^(0)C. What is the amount of heat required to raise the temperature of 1 kg of substance from 10^(@)C to 20^(@)C?

The specific heat of a substance varies as (3t^(2) + t) xx 10^(-3) "ca

1.	The specific heat of a substance varies as (3t^(2) + t) xx 10^(-3) "cal"//g- ^(0)C. What is the amount of heat required to raise the temperature of 1 kg of substance from 10^(@)C to 20^(@)C?
Answer» Solution :For small change in temperature dt, heat required , dQ =med t < br> `therefore Q = int_(t_(1))^(t_(2))` mcdt Given , m= 1000 g, `therefore Q= int_(10)^(20)1000(3t^(2) + t xx 10^(-3) dt =\|t^(3)+t^(2)/2\|_(10)^(20) -(20^(3) + 20^(2)/2) -(10^(3)+10^(2)/2)= 8200-1050=7150 "CAL".`